📶 Why Stack Radiating Elements?

Stacking multiple vertical radiators along the same axis — the core principle behind collinear antennas — concentrates energy toward the horizon and flattens the vertical radiation pattern. A simple quarter-wave whip (¼ λ) produces a lobe at approximately 25° elevation with a reference gain of 0 dBd. Upgrading to a half-wave (½ λ) shifts the main lobe down to ≈ 15° and yields a gain of about +2 dBd. By chaining together three identical and correctly phased sections, typical gains reach around +6 dBd, with a main lobe just 3–5° above the horizon.

This constructive superposition of fields is what makes collinear designs attractive for increasing horizontal range.

However, this gain does not scale indefinitely. Beyond a few sections, geometric and phase alignment errors accumulate, side lobes begin to grow, and mechanical constraints or signal cancellation reduce overall efficiency. That’s why most practical collinears stop at two or three (sometimes five for commercial device) radiating sections.

Radiation Angle vs Gain (Illustrative)

🛑📡The Non-Radiation of the Folded Stub: Physical Justification and Current Integral

In the folded stub (three parallel conductors connected by two 180° bends), the cancellation of radiation does not arise from differences in optical path: since the conductors are very close together (d ≪ λ), every point on the stub is virtually at the same distance from the far-field observer, so the geometric phases are aligned.

The real mechanism is linked to the current distribution: as you move along the stub, the current reverses direction at each change of conductor (up, down, up again). Mathematically, this is expressed by a far-field integral :

where I(z) alternates in sign along each straight segment due to the folded geometry.

As a result of this alternation (harmonic character of the current plus the inversion of its direction along the stub), the integral of the contributions from the three straight sections is nearly zero over the whole stub, and the bends only contribute negligibly : on the order of kd power 2.

In this image, the stub is visible, with the copper wire guided along the structure. On the right, a 4 mm brass tube is inserted into the PLA body. The tube is then crimped onto the copper wire using a crimping tool (if you don’t have one, a standard pair of pliers can be used instead).

In summary, the folded stub is almost electromagnetically silent, because the variation in current and the reversal of its direction within the stub enforce an almost complete cancellation of the far-field. This result is fundamental and is the same principle used in Franklin arrays and other phased-line antennas. Some commercial antenna designs also employ similar geometries for their stub.

🌀Capacitive Matching of the Radiating Element and Impedance Autotransformer

A vertical monopole antenna resonates ideally when it measures a quarter-wavelength (¼ λ): at this length, the input impedance is largely resistive and well matched (typically 36 Ω with a perfect ground plane) and has very little reactive component. However, as soon as the element is lengthened beyond λ/4—up to about 5/8 λ, as is the case here for our first section to optimize the radiation pattern—the tip of the element accumulates significant charge, creating a capacitive reactance: the feedpoint “sees” a typical impedance of about...